Data detection in mimo systems with demodulation and tracking reference signals

ABSTRACT

What is disclosed is a method for wireless communication comprising receiving a wireless communication via a receiver of the mobile communication device, deriving a demodulation reference signal from a first plurality of symbols of the wireless communication; creating a channel estimation matrix using the demodulation reference signal; inverting the channel estimation matrix to obtain a channel pseudo-inverse matrix; deriving a tracking reference signal from a second plurality of symbols of the wireless communication; calculating a phase shift for one or more additional symbols based on the tracking reference signal; determining a corrected channel pseudo-inverse matrix for the one or more additional symbols by adjusting the channel pseudo-inverse matrix according to the calculated phase shift; and controlling the receiver to accomplish data detection using the corrected channel pseudo-inverse matrix on one or more orthogonal frequency division multiplexing subcarriers.

TECHNICAL FIELD

This Disclosure relates generally to methods and devices for MIMOdetection in wireless communication systems with phase tracking.

BACKGROUND

Linear detection or demodulation methods are methods for low complexitydetection of spatially multiplexed multiple-input and multiple-output(“MIMO”) systems. These methods typically include a zero-forcing (“ZF”)technique and a minimum mean square error (“MMSE”) technique. Thesedetection methods require a computationally rigorous calculation.Moreover, in a MIMO system, the receiving component of a wirelesscommunication generally performs a data detection for each orthogonalfrequency division multiplexing (“OFDM”) symbol in a subframe, whichresults in a frequently repeated, computationally complex calculationthat demands significant computational resources.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, like reference characters generally refer to the sameparts throughout the different views. The drawings are not necessarilyto scale, emphasis instead generally being placed upon illustrating theprinciples of the Disclosure. In the following description, variousaspects of the Disclosure are described with reference to the followingdrawings, in which:

FIG. 1 shows a first arrangement for a MIMO transmission and receptionsystem;

FIG. 2 shows a second arrangement for a MIMO transmission and receptionsystem;

FIG. 3 shows a symbol constellation map;

FIG. 4 shows a MIMO receiver device;

FIG. 5 shows a conventional method of MIMO detection for systems withtracking information;

FIG. 6 shows a method of MIMO detection whereby partial MIMO detectionis performed before assessment of tracking;

FIG. 7 shows a subframe with a single demodulation reference signal(“DMRS”) transmission and a tracking reference signal (“TRS”) over time;

FIG. 8 shows an apparatus for radio communication;

FIG. 9 shows a method for radio communication;

FIG. 10 shows a conventional system for matrix decompensation;

FIG. 11 shows a system for matrix decompensation with trackinginformation; and

FIG. 12 shows a method for matrix decomposition with trackinginformation.

DESCRIPTION

The following detailed description refers to the accompanying drawingsthat show, by way of illustration, specific details and aspects in whichthe Disclosure may be practiced.

The word “exemplary” is used herein to mean “serving as an example,instance, or illustration.” Any embodiment or design described herein as“exemplary” is not necessarily to be construed as preferred oradvantageous over other embodiments or designs.

The words “plural” and “multiple” in the description and the claimsexpressly refer to a quantity greater than one. Accordingly, any phrasesexplicitly invoking the aforementioned words (e.g. “a plurality of[objects]”, “multiple [objects]”) referring to a quantity of objectsexpressly refers more than one of the said objects. The terms “group(of)”, “set [of]”, “collection (of)”, “series (of)”, “sequence (of)”,“grouping (of)”, etc., and the like in the description and in theclaims, if any, refer to a quantity equal to or greater than one, i.e.one or more. The terms “proper subset”, “reduced subset”, and “lessersubset” refer to a subset of a set that is not equal to the set, i.e. asubset of a set that contains less elements than the set.

It is appreciated that any vector and/or matrix notation utilized hereinis exemplary in nature and is employed solely for purposes ofexplanation. Accordingly, it is understood that the approaches detailedin this disclosure are not limited to being implemented solely usingvectors and/or matrices, and that the associated processes andcomputations may be equivalently performed with respect to sets,sequences, groups, etc., of data, observations, information, signals,etc. Furthermore, it is appreciated that references to a “vector” mayrefer to a vector of any size or orientation, e.g. including a 1×1vector (e.g. a scalar), a 1×M vector (e.g. a row vector), and an M×1vector (e.g. a column vector). Similarly, it is appreciated thatreferences to a “matrix” may refer to matrix of any size or orientation,e.g. including a 1×1 matrix (e.g. a scalar), a 1×M matrix (e.g. a rowvector), and an M×1 matrix (e.g. a column vector).

A “circuit” as user herein is understood as any kind oflogic-implementing entity, which may include special-purpose hardware ora processor executing software. A circuit may thus be an analog circuit,digital circuit, mixed-signal circuit, logic circuit, processor,microprocessor, Central Processing Unit (“CPU”), Graphics ProcessingUnit (“GPU”), Digital Signal Processor (“DSP”), Field Programmable GateArray (“FPGA”), integrated circuit, Application Specific IntegratedCircuit (“ASIC”), etc., or any combination thereof Any other kind ofimplementation of the respective functions which will be described belowin further detail may also be understood as a “circuit.” It isunderstood that any two (or more) of the circuits detailed herein may berealized as a single circuit with substantially equivalentfunctionality, and conversely that any single circuit detailed hereinmay be realized as two (or more) separate circuits with substantiallyequivalent functionality. Additionally, references to a “circuit” mayrefer to two or more circuits that collectively form a single circuit.

As used herein, “memory” may be understood as a non-transitorycomputer-readable medium in which data or information can be stored forretrieval. References to “memory” included herein may thus be understoodas referring to volatile or non-volatile memory, including random accessmemory (“RAM”), read-only memory (“ROM”), flash memory, solid-statestorage, magnetic tape, hard disk drive, optical drive, etc., or anycombination thereof. Furthermore, it is appreciated that registers,shift registers, processor registers, data buffers, etc., are alsoembraced herein by the term memory. It is appreciated that a singlecomponent referred to as “memory” or “a memory” may be composed of morethan one different type of memory, and thus may refer to a collectivecomponent comprising one or more types of memory. It is readilyunderstood that any single memory component may be separated intomultiple collectively equivalent memory components, and vice versa.Furthermore, while memory may be depicted as separate from one or moreother components (such as in the drawings), it is understood that memorymay be integrated within another component, such as on a commonintegrated chip.

The term “base station” used in reference to an access point of a mobilecommunication network may be understood as a macro base station, microbase station, Node B, evolved NodeB (“Enb”), Home eNodeB, Remote RadioHead (“RRH”), relay point, etc., and may include base stationsimplemented with conventional base station architectures (e.g.distributed, “all-in-one”, etc.) and base stations implemented withcentralized base stations architectures (e.g. Cloud Radio Access Network(“Cloud-RAN”) or Virtual RAN (“Vran”)). As used herein, a “cell” in thecontext of telecommunications may be understood as a sector served by abase station. Accordingly, a cell may be a set of geographicallyco-located antennas that correspond to a particular sectorization of abase station. A base station may thus serve one or more cells (orsectors), where each cell is characterized by a distinct communicationchannel. Furthermore, the term “cell” may be utilized to refer to any ofa macrocell, microcell, femtocell, picocell, etc.

For purposes of this disclosure, radio communication technologies may beclassified as one of a Short Range radio communication technology,Metropolitan Area System radio communication technology, or CellularWide Area radio communication technology. Short Range radiocommunication technologies include Bluetooth, WLAN (e.g. according toany IEEE 802.11 standard), and other similar radio communicationtechnologies. Metropolitan Area System radio communication technologiesinclude Worldwide Interoperability for Microwave Access (“WiMax”) (e.g.according to an IEEE 802.16 radio communication standard, e.g. WiMaxfixed or WiMax mobile) and other similar radio communicationtechnologies. Cellular Wide Area radio communication technologiesinclude GSM, UMTS, LTE, LTE-Advanced (“LTE-A”), CDMA, WCDMA, LTE-A,General Packet Radio Service (“GPRS”), Enhanced Data Rates for GSMEvolution (“EDGE”), High Speed Packet Access (“HSPA”), HSPA Plus(“HSPA+”), and other similar radio communication technologies. CellularWide Area radio communication technologies also include “small cells” ofsuch technologies, such as microcells, femtocells, and picocells.Cellular Wide Area radio communication technologies may be generallyreferred to herein as “cellular” communication technologies. It isunderstood that exemplary scenarios detailed herein are demonstrative innature, and accordingly may be similarly applied to various other mobilecommunication technologies, both existing and not yet formulated,particularly in cases where such mobile communication technologies sharesimilar features as disclosed regarding the following examples.

The term “network” as utilized herein, e.g. in reference to acommunication network such as a mobile communication network,encompasses both an access section of a network (e.g. a radio accessnetwork (“RAN”) section) and a core section of a network (e.g. a corenetwork section). The term “radio idle mode” or “radio idle state” usedherein in reference to a mobile terminal refers to a radio control statein which the mobile terminal is not allocated at least one dedicatedcommunication channel of a mobile communication network. The term “radioconnected mode” or “radio connected state” used in reference to a mobileterminal refers to a radio control state in which the mobile terminal isallocated at least one dedicated uplink communication channel of amobile communication network.

Unless explicitly specified, the term “transmit” encompasses both direct(point-to-point) and indirect transmission (via one or more intermediarypoints). Similarly, the term “receive” encompasses both direct andindirect reception. The term “communicate” encompasses one or both oftransmitting and receiving, i.e. unidirectional or bidirectionalcommunication in one or both of the incoming and outgoing directions.

MIMO Wireless Communication Systems

MIMO systems may employ multiple transmit and receive antennas totransmit multiple data layers on a shared MIMO channel, i.e. a set ofshared time-frequency resources. Such MIMO systems may rely on thediffering spatial channels between each of the transmit and receiveantennas to allow the receiver to individually recover the transmitteddata layers from the signals received at the received antennas, whichmay each be composed of contributions from each transmit antenna thathave been altered by noise and other channel effects.

In a MIMO system, each transmit antenna may transmit a separate transmitsymbol using the same shared time-frequency resources (e.g. using thesame subcarrier or set of subcarriers during a common symbol period).Each receive antenna may then produce a separate receive symbol, whereeach receive symbol contains a contribution from each transmit symbolthat has been altered by the spatial channel between the correspondingreceive antenna and each transmit antenna. MIMO receivers may thenprocess the receive symbols to recover the original transmit symbols,which may include applying channel equalization based on channelestimates of each spatial channel in order to individually detect eachtransmit symbol from the receive symbols. In a multi-subcarrier MIMOcase such as for Orthogonal Frequency Division Multiple Access (“OFDMA”)or Single Carrier Frequency Division Multiple Access (“SC-FDMA”), eachMIMO transmit antenna may transmit a transmit symbol on each of aplurality of subcarriers that collectively compose the shared MIMOchannel.

MIMO systems may employ multiple transmitters and/or multiple receiversand/or multiple transceivers, and accordingly may be characterized asSingle-User MIMO (“SU-MIMO”) or Multi-User MIMO (“MU-MIMO”) systems.FIG. 1 shows MIMO system 100, which may be a basic 2×2 SU-MIMO systemincluding MIMO transmitter 110 composed of two transmit antennas 110 ₁and 110 ₂ and MIMO receiver 120 composed of two receive antennas 120 ₁and 120 ₂. As MIMO channel 130 is shared between a single transmitter(110) and single receiver (120), MIMO system 100 may be classified as anSU-MIMO system.

As shown in FIG. 1, transmitter 110 may transmit two data layers (Layer1 and Layer 2) on MIMO channel 130 to receiver 120. Transmitter 110 mayapply channel coding, scrambling/interleaving, modulation, and antennamapping on the original data layers to generate transmit symbols s₁ ands₂ that collectively compose transmit vector s=[s₁ s₂]^(T). Transmitter110 may then transmit each of transmit symbols s₁ and s₂ via transmitantennas 110 ₁ and 110 ₂. Transmit symbols s₁ and s₂ may propagatethrough MIMO channel 130 and subsequently be received by receiveantennas 120 ₁ and 120 ₂, which may subsequently produce receive symbolsy₁ and y₂ constituting receive symbol vector y=[y₁ Y₂]^(T). As shown inFIG. 1, both receive symbols y₁ and y₂ may contain contributions fromboth transmit symbols s₁ and s₂, which may be characterized by thechannel matrix H of MIMO channel 130 where H=[h_(1,1) h_(1,2); h_(2,1)h_(2,2)] and each h_(i,j) for i,j=1,2 is a complex-valued termcharacterizing the wireless channel response between transmit antenna110 _(j) and receive antenna 120 _(i). Receiver 120 may recover theoriginal data layers by applying MIMO detection on receive vector y.

Including the contribution from additive noise modeled as n=[n₁ n₂]^(T)in MIMO channel 130, MIMO system 100 may be modeled according to H, s,y, and n as follows:

y=Hs+n   (1)

MIMO system 100 and Equation (1) may be analogously expanded to any M×NMIMO system with N transmit antennas (and corresponding transmit symbolvector s=[s₁, . . . , s_(N)]^(T)) and M receive antennas (andcorresponding receive symbol vector y=[y₁, . . . , y_(M)]^(T)), where Hdenotes the M×N complex channel matrix composed of complex channelresponse elements h_(i,j), i=1, . . . , M, j=1, . . . , N, s denotes thecomplex transmitted symbol vector, n denotes the complex additive noise,and y denotes the complex received noisy symbol vector.

Equation (1) may similarly hold in a MU-MIMO system employing multipletransmitters and/or receivers. FIG. 2 depicts MIMO system 200, which maybe an MU-MIMO system including two MIMO transmitters and one MIMOreceiver. As opposed to a single transmitter and single receiver eachwith multiple respective transmit and receive antennas, MU-MIMO system200 may include two MIMO transmitters 210 and 212 which may eachtransmit a respective data layer as s₁ and s₂ over transmit antennas 210₁ and 212 ₂, respectively. MIMO receiver 220 may then receive transmitsymbols s₁ and s₂ as noisy receive symbols y₁ and y₂ followingpropagation over MIMO channel 230, and may similarly perform MIMOdetection on y using a channel matrix H that characterizes MIMO channel230 to recover the original data layers. Further variations includingincreasing the total number N and M of transmit and receive antennas(where M≥N), e.g. two transmit antennas at each of MIMO transmitters 210and 212 and four receive antennas at MIMO receiver 220, reversing thedirection (e.g. with a single MIMO transmitter and multiple MIMOreceivers), and/or employing both multiple transmitters and multiplereceivers to share the MIMO channel are also within the scope of thepresent disclosure.

As shown in FIGS. 1 and 2, MIMO transmitters may apply one or more ofchannel coding, scrambling/interleaving, modulation, and antennamapping/precoding (for a MIMO transmitter with multiple transmitantennas) to the data layers prior to wireless MIMO transmission. Thechannel coding blocks of MIMO transmitters 110, 210, and 212 may receivea data layer and encode the data layer using a specific coding scheme toproduce an encoded digital stream that may allow for a MIMO receiver tocorrect transmission errors. The scrambling/interleaving blocks may thenperform interleaving and/or scrambling in order to re-arrange the bitsof the encoded digital stream according to a specificscrambling/interleaving scheme. The modulation blocks may then receivethe encoded and scrambled/interleaved digital stream and apply symbolmapping to convert the digital stream into a stream of complexmodulation symbols, where each of the modulation symbols represents oneor more bits of the encoded and scrambled/ interleaved digital stream.If multiple transmit antennas are present, e.g. for MIMO transmitter110, the antenna mapping block may apply an antenna mapping or precodingscheme to map each complex modulation symbol across the transmitantennas.

Each transmit symbol s_(j), j=1, . . . , N, of s and receive symboly_(i), i=1, . . . , M, of y may thus be a complex-valued symbolaccording to the particular modulation scheme employed by MIMO system100, where the receive symbols of y may be corrupted by channel effectsand noise. FIG. 3 shows constellation diagram 300 illustratingconstellation points (+1−1j), (+1+1j), (−1−1j), and (−1+1j) for a4-Quadrature Amplitude Modulation (“4-QAM”) scheme, where eachconstellation point may be a complex number with a real and imaginarycomponent. The set of constellation points may be denoted asconstellation

, where

={+1−1j, +1 +1j, −1−1j, −1 +1j} for the 4-QAM scheme depicted in FIG. 3.An analogous set of constellation points

may similarly be given for any modulation scheme, where the particularconstellation points of

will depend on the specific characteristics of the modulation scheme.Symbol vector s may thus be a vector of N symbols, where each symbolcorresponds to a particular constellation point of

, i.e. s ∈

^(N).

A modulation block such as depicted in MIMO transmitters 110, 210, and212 may receive a stream of digital input bits, partition the digitalstream into blocks, and map each blocks to a constellation point toproduce a corresponding complex symbol for each block. In the exemplary4-QAM case depicted in FIG. 3, a modulator may partition a digitalstream into two-bit blocks and map each two bit block (b₁b₂) toconstellation

as

(00)→(1+1j)

(01)→(1−1j)

(10)→(−1+1j)

(11)→(−1−1j)   (2)

The modulator may thus map the digital input stream to a stream ofcomplex modulation symbols, where each modulation symbol represents oneor more bits of the digital input stream according to the block size.Such complex modulation symbols (after precoding, if applicable) may besubsequently modulated on in-phase and quadrature (“IQ”) carriersaccording to the respective real and imaginary parts of each modulationsymbol and transmitted as transmit vector s over the transmit antennas.

MIMO receivers such as MIMO receivers 120 and 220 may thus seek torecover the individual data layers of s from the noisy receive symbolsof y obtained at receive antennas 120 _(i). MIMO receiver 120/220 mayperform such MIMO detection by applying a MIMO equalization (“EQ”)filter derived from the channel estimates for the individual spatialchannels of H. Specifically, MIMO receiver 120/220 may obtain a channelestimate for each spatial channel of H and generate a MIMO EQ filterthat MIMO receiver 120/220 may apply to receive vector y in order torecover an estimate ŝ for s. Application of such a MIMO EQ filter maythus allow a MIMO receiver to isolate an estimate for each transmitsymbol of s from the receive symbols of y, thus “detecting” the originaltransmit symbols and enabling MIMO receiver 120/220 to recover theoriginal data layers.

MIMO receiver 120/220 may perform MIMO detection using any of a numberof different algorithms.

Linear MIMO detectors such as zero-forcing (“ZF”) and Minimum MeanSquare Error (“MMSE”) detectors may be used to perform MIMO detection.For such linear detectors, MIMO receiver 120/220 may obtain a MIMO EQfilter matrix W any apply W to y as follows to obtain estimated transmitvector ŝ as

ŝ=Wy   (3)

where W is a matrix characterizing a linear filter operation.

ZF and MMSE detectors may differ in the selection of the lineartransformation matrix W, which in both cases may involve a linearmanipulation of channel matrix H. In a ZF and an MMSE detector, W isgiven as follows:

W ^(ZF)=(H ^(H) H)⁻¹ H ^(H)   (4)

W ^(MMSE)=(H ^(H) H+σ² I _(N))⁻¹ H ^(H)   (5)

respectively, where A^(H) denotes the Hermitian transpose of A, σ² isthe noise variance, and I_(N) denotes the N×N identity matrix. W^(MMSE)may be written as either W^(MMSE)=(H^(H)H+σ²I_(N))⁻¹H^(H)) orW^(MMSE)=H^(H)(HH^(H)+Nσ²I_(N))⁻¹.

Although either MMSE or ZF may be used for linear detection, they do notcorrect for phase shift, and therefore, and especially in a 5G context,they will yield results that must be subject to additional computationto assess and correct for phase shift.

FIG. 4 shows an internal configuration of MIMO receiver 400. As shown inFIG. 4, MIMO receiver 400 may include antenna array 402, radio frequency(“RF Frontend”) processing circuit 404, and baseband processing circuit406, which may be composed of preprocessing circuit 408, MIMO symboldetection circuit 410, channel estimation circuit 412, and basebandcontrol circuit 414.

MIMO receiver 400 may be realized in a wireless communication device. Ina cellular communication context, MIMO receiver 400 may be implementedas either a downlink MIMO receiver or an uplink MIMO receiver. In adownlink MIMO receiver implementation, MIMO receiver 400 may beimplemented at a mobile terminal and may receive downlink MIMO signalsfrom one or more base stations over a cellular communication network,such as e.g. on a shared OFDM MIMO channel in which shared discretesubcarriers compose the MIMO channel. MIMO receiver 400 may thus becontained in a single device, e.g. a mobile phone or similar mobileterminal device. Alternatively, in an uplink MIMO receiverimplementation, MIMO receiver 400 may be implemented at a base stationand may receive uplink MIMO signals from one or more mobile terminals,e.g. on a shared Single Carrier Frequency Division Multiple Access(“SC-FDMA”) MIMO channel that similarly employs shared discretesubcarriers for the MIMO channel after uplink SC-FDMA symbols have beenspread across the shared subcarriers. In such an uplink MIMO context,MIMO receiver 400 may be implemented as part of a distributed basestation architecture where the individual components of MIMO receiver400 depicted in FIG. 4 may be distributed between an antenna array(containing antenna array 402), a Remote Radio Unit (RRU; containing RFprocessing circuit 404 and optionally preprocessing circuit 408), and aBaseband Unit (BBU; containing baseband processing circuit 406optionally absent preprocessing circuit 408). MIMO receiver 400 mayalternatively be implemented as part of a Cloud-RAN base stationarchitecture in which baseband processing circuit 406 is implemented ata centralized location serving numerous the RRUs from numerous differentbase stations. MIMO receiver 400 as detailed herein is thus not limitedto any particular uplink/downlink context or device architecture. MIMOreceiver 400 may include one or more additional components such asadditional hardware, software, or firmware elements includingprocessors/microprocessors, controllers/microcontrollers, memory, otherspecialty or generic hardware/processors/circuits, etc., in order tosupport a variety of additional operations. In particular in the contextof a mobile terminal device, MIMO receiver 400 may be included in amobile terminal device that also includes a variety of user input/outputdevices (display(s), keypad(s), touchscreen(s), speaker(s), externalbutton(s), camera(s), microphone(s), etc.), peripheral device(s),memory, power supply, external device interface(s), subscriber identifymodule(s) (SIM) etc., which may be further controlled by a centralprocessing element such as a mobile Application Processor (“AP”).

Expanding on the abridged description presented above regarding MIMOreceiver operation of receiver 120/220, MIMO receiver 400 may beconfigured to receive wireless signals, such as according to aparticular network access protocol or radio access technology (“RAT”)including any of LTE, WLAN/WiFi, UMTS, GSM, Bluetooth, CDMA. W-CDMA,etc. Antenna array 402 be composed of M antennas in accordance with anM×N MIMO system, where each antenna may receive wireless radio frequencysignals and provide resulting electrical signals to RF processingcircuit 404. RF processing circuit 404 may include various receptioncircuitry components, which may include analog circuitry configured toprocess externally received signals such as e.g. mixing circuity toconvert externally received RF signals to baseband and/or intermediatefrequencies. RF processing circuit 404 may also include amplificationcircuitry to amplify externally received signals, such as poweramplifiers (“PAs”) and/or Low Noise Amplifiers (“LNAs”). RF processingcircuit 404 may be a transceiver component, and accordingly may also beconfigured to transmit wireless signals via antenna array 402 includinge.g. MIMO transmission. However, for purposes of explanation the receivechain will be of primary focus herein.

Baseband processing circuit 406 may be configured to establish andsupport connections with one or more network terminals (e.g. mobileterminals or base stations depending on an uplink or downlink context)by transmitting and receiving wireless signals over a particularwireless communication network according to corresponding networkprotocols. Baseband control circuit 414 may be configured to control thevarious components of baseband processing circuit 406 according toparticular protocol stack of the wireless communication network, andaccordingly baseband control circuit 414 may be protocol processor (e.g.microprocessor) configured to execute protocol stack software and/orfirmware modules by retrieving corresponding program code from abaseband memory (not explicitly shown in FIG. 4) and operate inaccordance with control logic provided by the protocol stack softwareand/or firmware modules. Baseband control circuit 414 may thus beconfigured to execute Layer 1 (Physical or “PHY” layer), Layer 2, andLayer 3 protocol stack software and/or firmware modules and may furthercontrol other components of baseband processing circuit 406 includingPHY layer hardware of MIMO detection circuit 410, channel estimationcircuit 412, preprocessing circuit 408, RF transceiver 404, and antennaarray 402 in accordance with the protocol stack software and/or firmwaremodules.

RF processing circuit 404 may provide baseband processing circuit 406with M separate analog data streams, where each i-th data streamcorresponds to the i-th antenna of antenna array 402. Basebandprocessing circuit 406 may first preprocess the M analog data streams atpreprocessing circuit 408, which may include analog-to-digitalconversion and preliminary demodulation to produce receive vector y. Ina multi-subcarrier MIMO context, preprocessing circuit 408 may produce areceive vector y for each subcarrier, where each receive vector ycontains the noisy receive symbols received on the correspondingsubcarrier. For example, in an LTE context preprocessing circuit 408 mayapply a Fast Fourier Transform (“FFT”) as part of the preliminarydemodulation processing for OFDM (downlink) or SC-FDMA (uplink). As OFDMand SC-FDMA MIMO may include sharing multiple discrete subcarriers thateach contain a transmit symbol, preprocessing circuit 408 may produce aseparate receive vector y containing M complex noisy received symbolsfor each subcarrier shared as part of the MIMO channel. Accordingly, therelationship of Equation (1) may be re-expressed as

y _(k) =H _(k) s _(k) +n _(k) , k=1, . . . ,N _(SC)   (6)

where N_(SC) is the number of subcarriers of the shared MIMO channel(e.g. where N_(sc)=1 in a single subcarrier case or N_(SC)>1 in amulti-subcarrier case) and y_(k), H_(k), s_(k), and n_(k) respectivelyare the receive vector, channel matrix, transmit vector, and noisevector for the k-th subcarrier of the shared MIMO channel. MIMO receiver400 may thus apply MIMO detection to the receive vector y_(k) for eachsubcarrier to recover an estimate ŝ_(k) for the original transmitsymbols transmitted by the MIMO transmitters on each subcarrier. Whilethe following description assumes the same number of data layers perMIMO subcarrier, such may be further configured to utilize differentnumbers of data layers per MIMO subcarrier.

MIMO detection circuit 410 may thus apply MIMO detection to the receivevector y_(k) for each subcarrier to recover an estimate ŝ_(k) for theoriginal transmit symbols transmitted by the MIMO transmitters on eachsubcarrier, thus allowing MIMO detection circuit 410 to recover theoriginal data layers as transmitted by the MIMO transmitters. As receivevector y_(k) includes complex symbols from a single symbol period,preprocessing circuit 408 may produce such a receive vector y_(k) foreach symbol period (for each subcarrier) over an extended duration ofsymbol periods to reflect continuing reception of MIMO signals byantenna array 402 and RF transceiver 404. MIMO receiver 400 may thuscontinuously perform decoding of each received vector y_(k) over anextended period of time as detailed below for receive vectors y_(k) in asingle symbol period.

MIMO Channel Estimation

FIG. 5 500 shows a conventional method of channel estimation and symboldetection in a MIMO system with tracking. According to this method, theDMRS 501 is transmitted in a wireless communication. The DMRS 501 isreceived by the channel estimator 502, which assesses the DMRS 501 andoutputs a channel estimate matrix (“H”) 503, of H ∈

^(N) ^(r) ^(×N) ^(t) , where N_(r) is the number of receive antennaports and N_(t) is the number of transmit antenna ports (number of MIMOlayers). The tracking block 504 rotates the channel estimate matrix H503 by an estimated rotation matrix Θ_(i), which is outputted as H_(i)505. The MIMO detector 506 then equalizes received symbols x_(i) ∈

^(N) ^(r) ^(×1) in order to estimate transmitted symbols (QAMconstellations) c_(i) ∈

^(N) ^(t) ^(×1) 507. Mathematically, MIMO system for each symbol at theinput of receiver can be expressed as

$\begin{matrix}{x = {\begin{bmatrix}x_{1} \\\vdots \\x_{N_{r}}\end{bmatrix} = {{{\begin{bmatrix}h_{11} & \ldots & h_{1N_{t}} \\\vdots & \ddots & \vdots \\h_{N_{r}1} & \ldots & h_{N_{r}N_{t}}\end{bmatrix}\begin{bmatrix}c_{1} \\\vdots \\c_{N_{t}}\end{bmatrix}} + \begin{bmatrix}n_{1} \\\vdots \\n_{N_{r}}\end{bmatrix}} = {{Hc} + n}}}} & (7)\end{matrix}$

where n ∈

^(N) ^(r) ^(×1) is a noise vector.

In 5G discussions, a tracking reference signal (“TRS”), sometimesreferred as Phase Noise Compensation Reference Signal, is beingconsidered. This TRS allows for the tracking of the changing phase ofthe signal, where the main contributor of the changing phase is phasenoise. Hence, the channel estimate at i-th OFDM symbol Ĥ_(i) is given by

$\begin{matrix}{{\hat{H}}_{i} = {{\hat{H} \cdot {\hat{\Theta}}_{i}} = \begin{bmatrix}{{\hat{h}}_{11}e^{j\; {\hat{\theta}}_{1\; {(i)}}}} & \ldots & {{\hat{h}}_{1N_{t}}e^{j\; {{\hat{\theta}}_{N_{t}}{(i)}}}} \\\vdots & \ddots & \vdots \\{{\hat{h}}_{N_{r}1}e^{j\; {{\hat{\theta}}_{1}{(i)}}}} & \ldots & {{\hat{h}}_{N_{r}N_{t}}e^{j\; {\hat{\theta}}_{N_{t}{(i)}}}}\end{bmatrix}}} & (8)\end{matrix}$

where Ĥ is rotated by a TRS matrix{circumflex over (Θ)}_(i) of complexexponentials e^(j{circumflex over (θ)}) ^(nt) ^((i)) and “∘” denotes theHadamard product. Note that in other cases, {circumflex over (Θ)}_(i)may not be limited to a matrix of complex exponentials. Finally,conventional ZF and MMSE MIMO detectors calculate

ĉ _(i) _(ZF) =(Ĥ _(i) ^(H) Ĥ _(i))⁻¹ Ĥ _(i) ^(H) x _(i)   (9)

ĉ _(i) _(MMSE) =(Ĥ _(i) ^(H) Ĥ _(i) +{circumflex over (N)} ₀ I)⁻¹ Ĥ _(i)^(H) x _(i)   (10)

where {circumflex over (N)}₀ is an estimated noise power (assuming it isthe same for all received antenna ports), I is an identity matrix, and“()^(H)” denotes Hermitian (conjugate) transpose. Note that ZF detectorin Eq. (9) is equivalent to MMSE detector in Eq. (10) when {circumflexover (N)}₀=0.

MIMO Channel Estimation Using Tracking Data

FIG. 6, 600 shows a modified method of, and apparatus for, channelestimation and symbol detection, according to an aspect of theDisclosure. According to this method and/or apparatus, the DMRS 501 istransmitted in a wireless communication. The DMRS 501 is received by thechannel estimator 502, which assesses the DMRS 501 and outputs a channelestimate matrix (“H”) 503. A modified MIMO Detector I 601 assesses H andcalculates a pseudo inverse to determine F 603, where

F=(Ĥ ^(H) Ĥ+{circumflex over (N)} ₀ I)⁻¹ Ĥ ^(H)   (11)

The tracking block 504 assesses the tracking signals and determines aphase shift, and rotates F to correct for the phase shift, where thecorrected F is F_(i) 604, and where F_(i) is

F_(i)={circumflex over (Θ)}_(i) ^(H)F   (12)

The resulting F_(i) 604 along with received symbol x_(i) is assessed bythe Modified MIMO Detector II 602, which outputs a detected symbol c_(i)509. This results in a novel method to solve a linearized system withtracking property using either ZF or MMSE techniques described in,respectively, Eq.(9) and Eq.(10) by moving the most computationallyexpensive operations before tracking block 504. The exact method of thisoperation is somewhat dependent on the configuration of the system, andspecifically whether the transmitters and/or receivers are synchronous,and therefore it can be described in greater detail as follows.

Transmitter and Receiver Synchronization-Specific Adaptations

In systems with synchronous receivers and asynchronous transmitters,such as a downlink scenario when receiver has N_(r) synchronized receiveantenna ports and transmitters have N_(t) asynchronous antenna ports,Eq.(8) can be rewritten as matrix multiplication as follows:

Ĥ_(i)=Ĥ{circumflex over (Θ)}_(i)   (13)

where {circumflex over (Θ)}_(i) is a square diagonal matrix with maindiagonal [e^(j{circumflex over (θ)}) ¹ ^((i)),e^(j{circumflex over (θ)}) ² ^((i)), . . . e^(j{circumflex over (θ)})^(Nt) ^((i))]^(T). Since {circumflex over (Θ)}_(i) is unitary({circumflex over (Θ)}_(i) ⁻¹={circumflex over (Θ)}_(i) ^(H)), areduced-complexity solution can be found as

$\begin{matrix}{{c_{i} = {{\left( {{{\hat{\Theta}}_{i}^{H}{\hat{H}}^{H}\hat{H}\; {\hat{\Theta}}_{i}} + {{\hat{N}}_{0}I}} \right)^{- 1}{\hat{\Theta}}_{i}^{H}{\hat{H}}^{H}x_{i}} = {{{\hat{\Theta}}_{i}^{H}\mspace{11mu} \underset{\underset{F}{}}{\left( {{{\hat{H}}^{H}\hat{H}} + {{\hat{N}}_{0}I}} \right)^{- 1}{\hat{H}}^{H}}x_{i}} = {{\underset{\underset{F_{i}}{}}{{\hat{\Theta}}_{i}^{H}\; F}\; x_{i}} = {F_{i}x_{i}}}}}},} & (14)\end{matrix}$

where F is calculated once (once per subframe for 5G systems) using amodified MIMO detector that is subdivided into 1^(st) F-calculationpart, 2^(nd) ĉ_(i)-calculation part and a modified tracking block inbetween that calculates F_(i).

In systems with asynchronous receivers and synchronous transmitters,such as in some uplink scenarios, the receiver may have N_(r)asynchronous (distributed) receive antenna ports and the transmittersmay have N_(t) synchronized antenna ports. Under these circumstances,the estimated channel matrix can be written as

Ĥ_(i)={circumflex over (Φ)}_(i)Ĥ  (15)

where {circumflex over (Φ)}_(i) is a square diagonal matrix with maindiagonal [e^(j{circumflex over (φ)}) ¹ ^((i)),e^(j{circumflex over (φ)}) ² ^((i)), . . . , e^(j{circumflex over (φ)})² ^((i)), . . . , e^(j{circumflex over (φ)}) ^(Nr) ^((i))]^(T). Usingsimilar approach, a reduced-complexity solution can be found as

$\begin{matrix}{{\hat{c}}_{i} = {{\left( {{{\hat{H}}^{H}{\hat{\Phi}}_{i}^{H}{\hat{\Phi}}_{i}\hat{H}} + {{\hat{N}}_{0}I}} \right)^{- 1}{\hat{H}}^{H}{\hat{\Phi}}_{i}^{H}x_{i}} = {{\underset{\underset{F}{}}{\left( {{{\hat{H}}^{H}\hat{H}} + {{\hat{N}}_{0}I}} \right)^{- 1}{\hat{H}}^{H}}\; {\hat{\Phi}}_{i}^{H}x_{i}} = {{\underset{\underset{F_{i}}{}}{F\; {\hat{\Phi}}_{i}^{H}}\; x_{i}} = {F_{i}{x_{i}.}}}}}} & (16)\end{matrix}$

In systems with asynchronous receivers and asynchronous transmitters,then by combining equations (13) and (15),

Ĥ_(i)={circumflex over (Φ)}_(i)Ĥ{circumflex over (Θ)}_(i),   (17)

and a general reduced-complexity solution can be found as

$\begin{matrix}{{{\hat{c}}_{i} = {{\underset{\underset{F_{i}}{}}{{\hat{\Theta}}_{i}^{H}F\; {\hat{\Phi}}_{i}^{H}}\; x_{i}} = {F_{i}x_{i}}}},} & (18)\end{matrix}$

Noise-Balancing Detection Adaptations

Where the MMSE detector is a Noise-Balanced MMSE detector, a slightmodification may be used. The assumption in Eq. (10) that noise power isequal among all receive antenna ports is not always true. Hence, theestimated noise power {circumflex over (N)}₀ should be replaced withdiagonal matrix {circumflex over (N)}₀ of noise power estimates forN_(r) receive antenna ports with main diagonal [{circumflex over(N)}₀₍₁₎, {circumflex over (N)}₀₍₂₎, . . . {circumflex over (N)}_(0(N)_(r) ⁾]^(T). Since {circumflex over (N)}₀ is diagonal, the generalreduced-complexity solution in Eq. (18) holds true and can be written as

ĉ _(i)={circumflex over (Θ)}_(i) ^(H) F{circumflex over (Φ)} _(i) ^(H) x_(i)={circumflex over (Θ)}_(i) ^(H){(Ĥ ^(H) {circumflex over (N)} ₀ ⁻¹Ĥ+I)⁻¹ Ĥ ^(H) {circumflex over (N)} ₀ ⁻¹}{circumflex over (Φ)}_(i) ^(H)x _(i).   (19)

Moreover, all reduced-complexity solutions in Eq. (14) and (18) holdtrue as well.

Using matrix inversion lemma, an alternative form of reduced-complexitysolution for Eq. (19) can be written as

ĉ _(i)={circumflex over (Θ)}_(i) ^(H) F{circumflex over (Φ)} _(i) ^(H) x_(i)={circumflex over (Θ)}_(i) ^(H) {Ĥ ^(H)(ĤĤ ^(H) +{circumflex over(N)} ₀)⁻¹}{circumflex over (Φ)}_(i) ^(H) x _(i).   (20)

Where the MMSE detector is an MMSE-Interference Rejection Combining(“IRC” or “MMSE-IRC”) detector or enhanced MMSE-IRC detector withNetwork Assisted Interference Cancellation/Suppression (“NAICS”), anadditional term must be added to represent the estimated covariancematrix of interference plus noise from the j-th interfering transmittedand subject to the same rotations by matrices {circumflex over(Θ)}_(i)(j) and {circumflex over (Φ)}_(i), which can be written as

$\begin{matrix}{{\hat{R}}_{i} = {{{{\hat{\Phi}}_{i}\left( {{\sum\limits_{j}{{\hat{H}(j)}{{\hat{\Theta}}_{i}(j)}{{\hat{\Theta}}_{i}^{H}(j)}{{\hat{H}}^{H}(j)}}} + {\hat{N}}_{0}} \right)}{\hat{\Phi}}_{i}^{H}} = {{{{\hat{\Phi}}_{i}\left( \underset{\underset{R}{}}{{\sum\limits_{j}{{\hat{H}(j)}{{\hat{H}}^{H}(j)}}} + {\hat{N}}_{0}} \right)}{\hat{\Phi}}_{i}^{H}} = {{\hat{\Phi}}_{i}R\; {{\hat{\Phi}}_{i}^{H}.}}}}} & (21)\end{matrix}$

Hence, by incorporating this new term into Eq. (19)-(20), the generalreduced-complexity solution for MMSE-IRC detector can be written as

ĉ _(i)={circumflex over (Θ)}_(i) ^(H) F{circumflex over (Φ)} _(i) ^(H) x_(i)={circumflex over (Θ)}_(i) ^(H){(Ĥ ^(H) {circumflex over (R)} ⁻¹Ĥ+I)⁻¹ Ĥ ^(H) {circumflex over (R)} ⁻¹}{circumflex over (Φ)}_(i) ^(H) x_(i).   (22)

ĉ _(i)={circumflex over (Θ)}_(i) ^(H) F{circumflex over (Φ)} _(i) ^(H) x_(i)={circumflex over (Θ)}_(i) ^(H) {Ĥ ^(H)(ĤĤ ^(H) +{circumflex over(R)})⁻¹}{circumflex over (Φ)}_(i) ^(H) x _(i),   (23)

In FIG. 7, a radio communication subframe 700 is depicted, wherein saidsubframe comprises a plurality of rows and columns, each of whichfurther comprise a plurality of OFDM symbols 701. This figure shows theDMRS 702 being transmitted vertically across subcarriers once persubframe. This figure further shows a TRS 703 being transmitted overtime across a subcarrier.

FIG. 8 shows an apparatus for wireless communication, said apparatuscomprising an transceiver 801, configured to receive a wirelesscommunication 802, wherein the wireless communication further comprisesa demodulation reference signal and a tracking reference signal; asignal processing circuit 803 configured to create a channel estimationmatrix for the wireless communication; and a phase calculation circuit804 configured to calculate a phase shift of the wireless communicationusing a tracking reference signal; wherein the signal processing circuit803 creates a channel estimation matrix based on the receiveddemodulation reference signal and inverts the channel estimation matrixto obtain a channel pseudo-inverse matrix; wherein the phase calculationcircuit 804 calculates a phase shift for one or more additional symbolsbased on the tracking reference signal and determines a correctedchannel pseudo-inverse matrix by adjusting the channel pseudo-inversematrix according to the calculated phase shift; and wherein the signalprocessing circuit 803 performs data detection on one or more orthogonalfrequency division multiplexing subcarriers using the corrected channelpseudo-inverse matrix.

FIG. 9 shows a method adapted for performing MIMO detection in a mobilecommunication device 900, said method comprising performing wirelesscommunication via a transceiver of the mobile communication device 901;generating a demodulation reference signal based on a first plurality ofsymbols of the wireless communication 902; generating a channelestimation matrix based on the demodulation reference signal 903;inverting the channel estimation matrix to obtain a channelpseudo-inverse matrix 904; generating a tracking reference signal basedon a second plurality of symbols of the wireless communication 905;calculating a phase shift for one or more additional symbols based onthe tracking reference signal 906; determining a corrected channelpseudo-inverse matrix for the one or more additional symbols byadjusting the channel pseudo-inverse matrix according to the calculatedphase shift 907; and controlling the transceiver to perform datadetection on one or more orthogonal frequency division multiplexingsubcarriers based on the corrected channel pseudo-inverse matrix 908.

FIG. 10 shows a conventional method of matrix decomposition in a MIMOsystem with tracking. According to this method, the DMRS 1001 istransmitted in a wireless communication. The DMRS 1001 is received bythe channel estimator 1002, which assesses the DMRS 1001 and outputs achannel estimate matrix (“H”) 1003, of H ∈

^(N) ^(r) ^(×N) ^(t) , where N_(r) is the number of receive antennaports and N_(t) is the number of transmit antenna ports (number of MIMOlayers). The tracking block 1004 rotates the channel estimate matrix H1003 by an estimated rotation matrix Θ_(i), which is outputted as H_(i)1005. The Matrix Processor 1006 then equalizes received symbols x_(i) ∈

^(N) ^(r) ^(×1) in order to estimate transmitted symbols (QAMconstellations) c_(i) ∈

^(N) ^(t) ^(×1) which are output as D_(i) 1007.

FIG. 11 shows a modified method of, and apparatus for, matrixdecomposition 1100, according to an aspect of the Disclosure. Accordingto this method and/or apparatus, the DMRS 1101 is transmitted in awireless communication. The DMRS 1101 is received by the channelestimator 1102, which assesses the DMRS 1001 and outputs a channelestimate matrix (“H”) 1103. A matrix processor 1104 assesses H 1103 andcalculates a decomposed matrix to determine D 1105. The modifiedtracking block 1106 assesses the tracking signals and determines a phaseshift, and rotates D to correct for the phase shift, where the correctedD 1105 is D_(i) 1107.

FIG. 12 shows a method of performing matrix decomposition in amultiple-input multiple-output system with tracking 1200, said methodcomprising receiving a wireless communication via a receiver of a mobilecommunication device 1201;

-   deriving a demodulation reference signal from a first plurality of    symbols of the wireless communication 1202;-   creating a channel estimation matrix using the demodulation    reference signal 1203;-   calculating a decompensation matrix of the channel estimation matrix    1204;-   deriving a tracking reference signal from a second plurality of    symbols of the wireless communication 1205;-   calculating a phase shift for one or more additional symbols based    on the tracking reference signal 1205; and determining a corrected    decompensation matrix for the one or more additional symbols by    adjusting the decompensation matrix according to the calculated    phase shift 1206.

5G Development and Impact on MIMO Tracking and Detection

Among the advances in wireless communication is 5^(th) Generation MobileTechnology (“5G”). Although 5G is currently in development, and thestandards for 5G have not been finalized, an outline for 5G is beingsolidified, and there are several trends that have become apparent. Ofnote, 5G is likely to use much higher frequency wavelengths the LTE forwireless communication, potentially between 30 and 300 gigahertz, whichis a significant departure from the current wavelengths in LTE or priorlegacy Radio Access Technologies. In addition, 5G is likely to use asignificantly shorter subframe structure. For example, in LTE, a radiosubframe is 1 millisecond long. Although the 5G subframe length has notyet been fixed, the 5G subframe length is expected to be considerablyshorter than the 1 millisecond subframe length in LTE. The comparativelyshort subframe results in greater channel stability over the duration ofthe subframe, since a given subframe permits less time for a channel tochange or decay. According to one aspect of the Disclosure, the shortersubframe and higher frequency wavelengths permit a departure from theknown MIMO channel equalization procedure. In essence, this permits anovel channel estimation scheme that is designed to result insignificantly lower complexity of ZF or MMSE MIMO receivers. Accordingto an aspect of this Disclosure, the resulting ZF and/or MMSE MIMOdetection algorithm requires an order of magnitude less computation,which is expected to result in significant savings in chip area andpower.

According to another aspect of the disclosure, this proposed algorithmis not limited to 5G, but can rather be generalized to any so called“linear in parameters” system comprising a tracking property. Thisincludes any nonlinear model described as a linear system. Otherwisestated, this algorithm can be applied wherever a linear system comprisesa tracking signal that is transmitted over time.

Reducing Frequency of Pseudo-Inverse Calculations by Performing ChannelDetection Before Phase Rotation.

According to one aspect of the Disclosure, the resulting method orapparatus results in a computationally efficient method for detection ofMIMO systems with a tracking property. According to this Disclosure,tracking information is assessed to calculate a phase shift. Thiscalculation is performed after the channel for a wireless communicationis calculated via ZF or MMSE, and before the MIMO detector.

Conventional techniques find a solution of MIMO system irrespective ofthe system's tracking property. Accordingly, the channel estimation anddetection scheme must perform a computationally demanding calculationfor every set of inputs. In particular, portions of the MIMO detectioninvolve calculating a pseudo-inverse of the estimated channel matrix,which is a comparatively complex calculation that requires significantresources.

As a general matter, the pseudo-inverse can be calculated when the DMRSis received. Yet, where the 5G subframe length is much shorter, and inlight of the increased channel stability inherent in 5G technology, itcan be reasonably assumed that the channel will remain acceptably stablethroughout the duration of the subframe. In light of this assumedstability, the need to calculate the pseudo-inverse each OFDM symbol isgreatly reduced, and it becomes generally acceptable to calculate thepseudo-inverse only once per subframe. This can be performed in responseto a single DMRS transmission per subframe, as demonstrated in FIG. 7.

Although the channel is expected to be reasonably stable throughout thesubframe, it may be necessary to repeatedly correct for phase shiftthroughout the subframe. The comparatively higher frequencies plannedfor 5G transmission are more susceptible to phase noise than thefrequencies currently in use in LTE. The phase shift is not anticipatedto remain acceptably static throughout the duration of the subframe, andtherefore multiple phase shift corrections during the subframe may benecessary. The phase shift is assessed based on a TRS, which may betransmitted over time along a subcarrier, as shown in FIG. 7, or in anyother configuration of sufficient frequency to acceptably correct thephase shift. The TRS is assessed to calculate the phase shift in themanner described above, and the phase shift is then corrected through anappropriate rotation of the signal. The signal may be rotated for eachOFDM symbol over time, or as often as necessary. This method permits theMIMO detection to be separated from the phase shift correction, suchthat the pseudo-inverse, which may be performed only once per subframe,is performed with minimal frequency, while still permitting the frequentperformance of the comparatively computationally simple procedure ofphase shift correction.

MIMO detection is performed based on information received from the DMRS.The actual calculations have been mathematically described above and arewell-known. Although the term DMRS has been used in this context, theterm DMRS is used for purposes of convenience and is not intended tosuggest any specific standards or operations that specifically defineDMRS as a term of art. For the purposes of this Disclosure, the DMRS mayinclude any kind of demodulation reference signal that can be used forMIMO detection, whether in 5G, LTE, or a legacy RAT, or otherwise. Inthe event that further development in 5G standards change the substanceor content of DMRS, this Disclosure is intended to include any DMRS,DMRS-equivalent, or DMRS-similar signal from which the channel may bedetected.

This method is intended to work with a MIMO wireless communicationsystem; however, the name, MIMO, is not intended as a limitation forthis method's use. In the event that other wireless communicationsystems resembling MIMO are developed, or in the event that dissimilarsystems are developed, on which this Disclosure can be used for channelestimation and detection, this Disclosure should be understood toinclude any such system or systems.

In the course of a MIMO-type transmission, the DMRS and the TRS may betransmitted by, and/or received on, a plurality of antennas. This mayinclude a plurality or transmit antennas and/or a plurality of receiveantennas. These antennas may be synchronous or asynchronous, or in acombination of same. For example, in a downlink scenario, the transmitantennas may be asynchronous, and the receive antennas may besynchronous. In an uplink scenario, the transmit antennas may besynchronous, and the receive antennas may be asynchronous. All antennasmay be synchronous, or all antennas may be asynchronous, or anycombination of the foregoing. 5G communication generally assumestransmissions from a plurality of base stations which are likely to beasynchronous.

According to an aspect of the Disclosure, where the DMRS or the TRS aretransmitted, they may be transmitted from a plurality of transmissionantennas. This may be any number of the transmit antennas. Similarly,the DMRS or the TRS may be received by all or less than all of thereceive antennas.

According to another aspect of the Disclosure, the DMRS may betransmitted in the OFDM wireless communication. Specifically, the DMRSmay be transmitted within one or more OFDM symbols or one or morereference elements. According to one aspect of the Disclosure, the DMRSmay be transmitted once per subframe, as is shown in FIG. 7. The DMRSmay alternatively be transmitted at a greater or lesser frequency thanonce per subframe. For example, the DMRS may be transmitted at once perframe, rather than once per subframe, or in any other frequency greaterthan once per subframe. Similarly, the DMRS may be transmitted morefrequently than once per subframe. This may be appropriate in periods ofparticular channel instability. Where the DMRS is transmitted in excessof once per subframe, the MIMO detection may be configured to calculatethe pseudo-inverse and/or detect the channel with each received DMRStransmission, or less frequently, as is desired.

According to one aspect of the Disclosure, the DMRS may be transmittedfor each subcarrier, as is depicted in FIG. 7. Thus, the DMRS may betransmitted once per subframe, simultaneously among all of thesubcarriers. Alternatively, the DMRS may be transmitted for fewer thanall subcarriers in a given subframe. Where the DMRS for each subcarrieris not transmitted, an additional step of estimating the channel basedon channel estimation of adjacent or nearby subcarriers must beperformed. Such estimation is known and need not be described in furtherdetail.

The DMRS may be a single, frontloaded demodulation reference signal.This is congruent with the emerging 5G standards, and takes advantage ofthe shorter subframes and increased channel stability apparent with 5Gtechnology. The DMRS may be transmitted or received on a physical uplinkcontrol channel, the a physical uplink shared channel, or otherwise.

According to an aspect of the Disclosure, the TRS may be received oneach symbol of one or more subcarriers within a subframe. As displayedin FIG. 7, the TRS may be transmitted or received within a singlesubcarrier in a subframe over time. Where this occurs, a subcarrier maybe dedicated to transmission or reception of TRS information. Unlike theDMRS, which may be transmitted or received one or few times during asubframe, the TRS should be transmitted frequently or constantly topermit ongoing, repeated phase shift tracking and adjustment. Accordingto one aspect of the Disclosure, the TRS may be transmitted or receivedon the fourth through the fourteenth OFDM symbols of a single subcarrierwithin a subframe. According to another aspect of the Disclosure, theTRS may be transmitted on the third through thirteenths subframesymbols.

Once the DMRS is received, a channel estimator calculates a channelestimate matrix from the received demodulation reference signals.Typically, the quantity of rows of the channel estimation matrixcorresponds to the quantity of receive antenna ports for the wirelesscommunication, and the quantity of columns of the channel estimationmatrix corresponds to the quantity of transmit antenna ports for thewireless communication. Where it is desired to reverse or otherwisealter the construction of the channel estimation matrix, this can beachieved with corresponding modifications to the mathematical formulasprovided above.

Upon completion of a channel estimation, a channel equalization may beperformed to estimate the symbols transmitted. This may be achieved witha zero-forcing equalizer algorithm or a minimum mean square errorequalizer, or other suitable means. The MIMO detection may furthercomprise isolating each of the plurality of encoded signal data unitsfrom the combined signal data unit based on the channel estimates forthe plurality of encoded signal data units. Isolating each of theplurality of encoded signal data units from the combined signal dataunit based on the channel estimates for the plurality of encoded signaldata units may include generating an equalization filter based on thechannel estimates for the plurality of channels, and applying theequalization filter to the combined signal data unit to isolate each ofthe plurality of encoded signal data units from the combined signal dataunit.

According to another aspect of the Disclosure, the method of claim 1,further comprises a shared time-frequency channel, said sharedtime-frequency channel comprising a plurality of channels between aplurality of transmit points and a plurality of receive points, andwherein isolating each of the plurality of encoded signal data unitsfrom the combined signal data unit includes determining a channelestimate for each of the plurality of channels, and isolating each ofthe plurality of encoded signal data units from the combined signal dataunits based on the channel estimates for the plurality of channels.

According to another aspect of the disclosure, the TRS is transmittedand/or received as part of the wireless communication. This TRS may becalled a Phase Noise Compensation Reference Signal. The TRS may becalled other names, as created or adopted by the 5G standards, thestandards for future implementations of wireless communication or futureRAT implementations, industry standards, industry usage, common usage,or otherwise. The TRS comprises information to evaluate the phase shiftof the wireless communication. The phase shift may be created primarilyby phase noise. Although phase noise is not of paramount concern in LTEand other legacy RATs, the millimeter waves and/or higher transmissionfrequencies of 5G are significantly more susceptible to phase noise, andtherefore additional corrective measures for phase noise must be taken.

The phase noise correction using TRS described herein is appropriate foruse in a 5G wireless communication system. It is, however, not limitedto 5G, and it may be used in a linear system in which trackinginformation is available. This may include other wireless communicationformats that develop concurrently with, or in succession to 5G. This mayinclude future RATs that are developed subsequently to, or inalternative to, 5G.

As described above, the receive antennas receive a TRS, which comprisesdata to assess the phase noise and/or phase shift of the signal. Thereceive antennas transfer this data to a circuit that is configured toarrange this data into a TRS matrix.

With the TRS matrix available, a circuit rotates the detected channel bycalculating the Hadamard product of the channel estimation matrix andthe TRS matrix. This process corrects for the phase shift of thedetected channel. The independent stream of tracking information in theTRS permits the independent calculation of channel and phase shift. Thisindependent calculation permits the calculation of channel, which is asignificantly more computationally complex procedure, to be performedfewer times per subframe than the phase rotation. According to oneaspect of the Disclosure, the channel is calculated once per subframe,and the tracking information is assessed to rotate and correct the phaseshift multiple times per subframe. The phase rotation and correction canbe performed for each OFDM symbol in the subframe.

It is anticipated the frame and subframe structure of 5G will besignificantly shorter than the frame and subframe structure on LTE. ThisDisclosure is intended to be functional within such a shorter framestructure. It is anticipated that the 5G subframe may be significantlyshorter than one millisecond. This significantly shorter period permitsa number of advantages, including increased channel stability over thelength of the subframe. This increased channel stability over the lengthof the subframe permits fewer pseudo-inverse calculations for lineardetectors per subframe compared to LTE.

It is anticipated that the 5G standards will include channel estimationbased on the frame structure as depicted in Fig, 7, where there is areference or pilot signal, such as the DMRS, and a TRS is transmittedalong a time domain. For applications, such as linear detectors, theability to reduce the computationally demanding channel pseudo-inverseprocess provides a significant conservation of resources in processingpower. Rather than dedicating the computational resources for channelpseudo-inverse for each OFDM symbol, the channel can be detected lessoften, and the less computationally demanding step of applying trackingreference symbol information can instead be performed.

In the current wireless technology, each subframe comprises fourteensymbols in the x-axis, during each of which the pseudo-inverse iscalculated for MIMO detection. The ability to reduce the calculation ofthe pseudo-inverse from fourteen times per subframe to one time persubframe results in thirteen fewer pseudo-inverse computations persubframe, which is a significant computational savings. This processprovides results that are equivalent to the conventional methods butwith significantly reduced complexity and need for computationalresources.

The phase shift correction through analysis of the TRS and subsequentsignal rotation is designed to correct for phase shift of the wirelesscommunication as it occurs between the transmit source and the receivesource. As described above, said phase shift may result from phasenoise, to which the anticipated wavelengths for 5G are especiallysusceptible. Said phase shift may also result, in whole or in part, froma Doppler effect, arising out of a relative change in distance betweenthe transmit source and the receive source.

The transmission of wireless data according to this Disclosure,including the DMRS and the TRS, may occur in an uplink or a downlinkscenario. In an uplink scenario, a downlink device, such as for examplea user device, transmits wireless data to a wireless network. Accordingto one aspect of the disclosure, this may be a base station. In adownlink scenario, data is transmitted from a network or a base stationto a downlink device. Without limitation, such downlink devices mayinclude user equipment, cellular phones, smart phones, wearable devices,tablet computers, laptop computers, personal computers, automobiles,appliances, homes, a home management system, a positioning system, amapping system, or any other device to receive wireless communication ina downlink setting. It is expressly anticipated that the breadth and/orusage of wireless devices to receive wireless communication in adownlink setting will expand with the use of 5G and subsequent RATs. Assuch, nothing in this Disclosure should be interpreted as a limitationof this Disclosure as only applying to devices already in existence.

The wireless communication, channel estimation, MIMO symbol detection,phase shift calculation, phase shift correction, and decoding describedherein may be performed by a variety of means. They may be performed byan apparatus or collection of apparatuses, which are configured toperform the steps and calculations described herein. They may beperformed by a circuit or plurality of circuits, which are configured toperformed the steps and calculations described herein. They may beperformed by software or a machine readable medium. Said software ormachine readable medium may be located at the uplink or downlinklocation. The circuitry or software to perform these tasks may,according to one aspect of the Disclosure, be located in a modem orbaseband modem.

The wireless communication, channel estimation, MIMO symbol detection,phase shift calculation, phase shift correction, and decoding describedherein may specifically be performed by a device configured to performwireless communication over a 5G network. They may be performed by adevice configured to perform wireless communication over a MIMO network,or a network utilizing MIMO technology. This may include wherein aplurality of transmit points are a plurality of MIMO transmit antennasand a plurality of receive points are a plurality of MIMO receiveantennas.

The channel or channels over which the wireless communications areperformed may be a shared time-frequency channel, composed of aplurality of channels between a plurality of transmit points and aplurality of receive points, and wherein an equalization circuit isconfigured to isolate each of the plurality of encoded signal data unitsfrom the combined signal data unit by determining a channel estimate foreach of the plurality of channels, and isolating each of the pluralityof encoded signal data units from the combined signal data unit based onthe channel estimates for each of the plurality of channels.

The wireless communications may be performed wherein an equalizationcircuit is configured to isolate each of the plurality of encoded signaldata units from the combined signal data unit based on the channelestimates for the plurality of encoded signal data units by generatingan equalization filter based on the channel estimates for the pluralityof channels, and applying the equalization filter to the combined signaldata unit to isolate each of the plurality of encoded signal data unitsfrom the combined signal data unit.

According to another aspect of the Disclosure, the calculations hereincan optionally include wherein the equalization circuit is configured toprocess the combined signal data unit from the shared time-frequencychannel to obtain the plurality of encoded signal data units byisolating each of the plurality of encoded signal data units from thecombined signal data unit.

According to another aspect of the Disclosure, the description hereincan optionally include wherein the shared time-frequency channelcomprises a plurality of channels between a plurality of transmit pointsand a plurality of receive points, and wherein the equalization circuitis configured to isolate each of the plurality of encoded signal dataunits from the combined signal data unit by determining a channelestimate for each of the plurality of channels, and isolating each ofthe plurality of encoded signal data units from the combined signal dataunits based on the channel estimates for the plurality of channels.

Matrix Decompensation, Generally

The above method for linear detecting relies on calculating apseudo-inverse of the channel estimation matrix. One method ofcalculating a pseudo-inverse of the matrix is to rely on matrixdecomposition methods. Matrix decomposition can be used to simplify thecalculations in linear detection, above. Furthermore, matrixdecomposition can provide utility in other aspects of a MIMO system withtracking information.

A number of matrix decompositions are popular methods for processingspatially multiplexed MIMO systems. These decompositions typicallyinclude QR decomposition, LU decomposition, LDL decomposition, Choleskydecomposition, singular value decomposition (“SVD”), and eigenvaluedecomposition (“EVD”). For example, such useful matrix decompositionscan be used in MIMO systems in noise-whitening, precoding, detectionetc.

The 5G standards currently in development comprise elements that permita novel channel estimation scheme that may lead to a significantly lowercomplexity of such matrix decompositions as described in thisDisclosure. It will be shown that the proposed matrix decompositionmethods require an order of magnitude less computations and, hence, chiparea and power for MIMO systems with tracking property.

Matrix Decompensation for MIMO Linear Detection

The method of Linear Detection as described above can be used withmatrix decomposition for channel detection. In this case, the channelestimate matrix H_(i) at the i-th OFDM symbol is given as:

$\begin{matrix}{H_{i} = {{H \cdot \Theta_{i}} = \begin{bmatrix}{h_{11}e^{j\; \theta_{1\; {(i)}}}} & \ldots & {h_{1N_{t}}e^{j\; {\theta_{N_{t}}{(i)}}}} \\\vdots & \ddots & \vdots \\{h_{N_{r}1}e^{j\; {\theta_{1}{(i)}}}} & \ldots & {h_{N_{r}N_{t}}e^{j\; \theta_{N_{t}{(i)}}}}\end{bmatrix}}} & (24)\end{matrix}$

where H is rotated by TRS matrix Θ_(i) of complex exponentials e^(jθ)^(t) ^((i)) and “∘” denotes the Hadamard product. Note that in othercases, Θ_(i) may not be limited to a matrix of complex exponentials.Another important matrix often used in MIMO systems is a Gram matrix

G _(i) =H _(i) ^(H) H _(i)=(H∘Θ_(i))^(H) H∘Θ_(i)=Θ_(i) ^(H) ∘H ^(H)H∘Θ_(i)=Θ_(i) ^(H) ∘G∘Θ_(i)   (25)

Conventional MIMO systems perform matrix decompositions of H_(i) andG_(i) matrices at each i-th OFDM symbol, while the proposed method insubsequent Section requires substantially less computations.

To use matrix decomposition to determine the channel, we turn to thematrix multiplications:

H_(i)=Φ_(i)HΘ_(i)   (26)

where Θ_(i) is a square diagonal matrix with main diagonal[|θ₁(i)|e^(j∠θ) ¹ ^((i)), . . . , |θ_(N) _(t) (i)|e^(j∠θ) ^(Nt)^((i))]^(T) and Φ_(i) is a square diagonal matrix with main diagonal[|φ₁(i)|e^(j∠φ) ¹ ^((i)), . . . , |φ_(N) _(r) (i)|e^(j∠φ) ^(Nr)^((i))]^(T), whereby, at this point, Eq. (25) can be rewritten as:

G _(i) =H _(i) ^(H) H _(i)=(Φ_(i) HΘ _(i))^(H)Φ_(i) HΘ _(i)=Θ_(i) ^(H) H^(H) P _(Φ) _(i) HΘ _(i),   (27)

where P_(Φ) _(i) =Φ_(i) ^(H)Φ_(i) ∈

^(N) ^(r) ^(×N) ^(r) is a square diagonal matrix. Typically, Φ_(i) is aunitary (complex exponentials on diagonal) and, hence, P_(Φ) _(i) equalto identity matrix P_(Φ) _(i) =I. Then, a simplified form of Gram matrixG_(i) in Eq.(27) can be expressed as

G_(i)′=Θ_(i) ^(H)H^(H)HΘ_(i)=Θ_(i) ^(H) G′Θ_(i)   (28)

Reduced-Complexity QR (Orthogonal Matrix and Upper Triangular Matrix)and Lower Upper Decompensation (“LU Decomposition”)

QR decomposition decomposes matrix A into a product A =QR, where Q is anorthogonal matrix and R is an upper triangular matrix. QR decompositionis often used to solve the linear least squares problem, and is thebasis for a particular eigenvalue algorithm, the QR algorithm.

Assuming that inputs for QR decomposition are defined by Eq.(26) andproperties of Θ_(i) and Φ_(i), a reduced-complexity QR decomposition canbe written as

qr(H _(i))=Q _(i) R _(i)=Φ_(i) qr(H)Θ_(i)=Φ_(i) QRΘ _(i)   (29)

where Q is a N_(r)×N_(r) complex-valued unitary matrix and R is aN_(r)×N_(t) upper-triangular matrix with real-valued main diagonal. Amore general Eq.(29) can be applied to Eq.(28) as well.

Similarly, a reduced-complexity LU decomposition can be written as

lu(H _(i))=L _(i) U _(i)=Φ_(i) lu(H)Θ_(i)=Φ_(i) LUΘ _(i)   (30)

where L is a N_(r)×N_(t) lower triangular matrix and U is a N_(t)×N_(t)upper-triangular matrix. Essentially, any Gaussian elimination typedecomposition can be represented in such a way.

Reduced-Complexity Cholesky and LDL Decompositions

A Cholesky decomposition allows for the decomposition of a Hermitian,positive-definite matrix, such that decomposition yields a product of alower triangular matrix and the conjugate transpose of the lowertriangular matrix. An LDL composition is a similar form of decompositionusing a lower unit triangular matrix and a diagonal matrix. Unlike QRand LU-like decompositions described above, both Cholesky and LDLdecompositions require a matrix to be decomposed to be positivedefinite. Hence, this can be applied to Hermitian G_(i), which is, ingeneral, a positive-semidefinite matrix, but this property can berelaxed to suffice Cholesky and LDL decomposition requirements. Ageneral reduced-complexity Cholesky-like decomposition can be derivedusing QR as

chol(G _(i))=Θ_(i) ^(H) qr(H ^(H))P _(Φ) _(i) qr(H)Θ_(i)=Θ_(i) ^(H) R^(H) Q ^(H) P _(Φ) _(i) QRΘ _(i)   (31)

Using Eq.(28) and result of Eq.(31), a reduced-complexity Cholesky andLDL decompositions for simplified G_(i)′ can be calculated directly as

chol(G _(i)′)={tilde over (R)} _(i) ^(H) {tilde over (R)} _(i)=Θ_(i)^(H) chol(G′) Θ_(i)=Θ_(i) ^(H) {tilde over (R)} ^(H) {tilde over (R)}Θ_(i)   (32)

ldl(G _(i)′)={tilde over (L)} _(i) D _(i) {tilde over (L)} _(i)^(H)=Θ_(i) ^(H) ldl(G′)Θ_(i)=Θ_(i) ^(H) {tilde over (L)}{tilde over(D)}{tilde over (L)} ^(H)Θ_(i)   (33)

where {tilde over (R)} is a N_(t)×N_(t) upper-triangular matrix withreal-valued main diagonal, {tilde over (L)} is a N_(t)×N_(t) lowertriangular matrix with all 1's on main diagonal and D is a N_(t)×N_(t)real-valued diagonal matrix.

Reduced-Complexity EVD and SVD

SVD is a general decomposition that can be applied to rectangularmatrices. Therefore, a reduced-complexity SVD applied to matrix in Eq.(26) can be written as

svd(H _(i))=U _(i)Σ_(i) S _(i) ^(H)=Φ_(i) svd(H)Θ_(i)=Φ_(i) UΣS^(H)Θ_(i)   (34)

where U is a N_(r)×N_(r) complex-valued unitary matrix of left-singularvectors, Σ is a N_(r)×N_(t) diagonal matrix of real non-negativesingular values, and S is a N_(t)×N_(t) complex-valued unitary matrix ofright-singular vectors.

EVD requires a being decomposed matrix to be positive definite. Hence,we can apply it to Hermitian G_(i) and a reduced-complexity EVD-likedecomposition can be derived using SVD as

evd(G _(i))=Θ_(i) ^(H) svd(H ^(H))P _(Φ) _(i) svd(H)Θ_(i)=Θ_(i) ^(H) SΣ^(H) U ^(H) P _(Φ) _(i) UΣS ^(H)Θ_(i)   (35)

Using Eq.(28) and result of Eq.(35), EVD for simplified matrix G_(i)′can be directly calculated as

evd(G _(i)′)=V _(i)Λ_(i) V _(i) ⁻¹=Θ_(i) ^(H) evd(G′)Θ_(i)=Θ_(i) ^(H)VΛV ⁻¹Θ_(i)=Θ_(i) ^(H) VΛV ^(HΘ) _(i),    (36)

where V is a N_(t)×N_(t) matrix of eigenvectors and Λ is a N_(t)×N_(t)diagonal matrix of real non-negative eigenvalues. Matrix V here isunitary and, hence, V⁻¹=V^(H).

Further Examples of Applications for MIMO Systems with Tracking

Matrix decompensation using tracking information is not limited toapplication in linear detection, but can also be used in otherapplications related to MIMO. The following examples are additional MIMOapplications for which matrix decompensation can be used.

Noise Whitening Filter

Typical noise whitening filter applies a square root matrix of positivedefinite G_(i) or simplified G_(i)′ using either QR decomposition(Eq.(29)) or Cholesky decomposition (Eq. (32)) as

$\begin{matrix}{\mspace{79mu} {G_{i}^{1/2} = {{{qr}\left( H_{i} \right)} = {{Q_{i}R_{i}} = {{\Phi_{i}{{qr}(H)}\Theta_{i}} = {\Phi_{i}{QR}\; \Theta_{i}}}}}}} & (37) \\{{\left( G_{i}^{\prime \; {1/2}} \right)^{H}\left( G_{i}^{\prime \; {1/2}} \right)} = {{{chol}\left( G_{i}^{\prime} \right)} = {{{\overset{\sim}{R}}_{i}^{H}{\overset{\sim}{R}}_{i}} = {{\Theta_{i}^{H}{{chol}\left( G^{\prime} \right)}\Theta_{i}} = {\left( {\overset{\sim}{R}\; \Theta_{i}} \right)^{H}{\left( {\overset{\sim}{R}\; \Theta_{i}} \right).}}}}}} & (38)\end{matrix}$

Maximum Likelihood and Tree Search Detectors

These types of detectors typically transform original minimizationmetric ∥x_(i)−H_(i)c_(i)∥² into a modified metric ∥Q_(i)^(H)x_(i)−R_(i)c_(i)∥² using QR decomposition. Then, areduced-complexity metric can be written as

∥Q _(i) ^(H) x _(i) −R _(i) c _(i)∥² =∥Q ^(H)Φ_(i) ^(H) x _(i) −RΘ _(i)c _(i)∥².   (39)

Pseudo-Inverse and Linear Detectors

Linear detectors like MMSE/ZF detectors are calculating pseudo-inversematrix F_(i). It can be shown that for systems with tracking suchpseudo-inverse matrix F_(i) can be calculated with reduced complexity as

F_(i)=Θ_(i) ^(H)FΦ_(i) ^(H)   (40)

where F=(H^(H)H+N₀I)⁻¹H^(H) for MMSE detector. In practice,pseudo-inverse matrix F is calculated using one of the matrixdecompositions described above. For example, using LDL decomposition

F=(H ^(H) H+N ₀ I)⁻¹ H ^(H)=(LDL ^(H))⁻¹ H ^(H) =L ^(−H) D ⁻¹ L ⁻¹ H^(H)   (41)

Assuming H_(i) ^(H)=Θ_(i) ^(H)H^(H)Φ_(i) ^(H) and P_(Φ) _(i) =I, resultof Eqs.(40)-(41) can be obtained explicitly using Eq.(32) as

$\begin{matrix}{F_{i} = {{L_{i}^{- H}D_{i}^{- 1}L_{i}^{- 1}H_{i}^{H}} = {{\left( {{\Theta_{i}^{H}H^{H}\Phi_{i}^{H}\Phi_{i}H\; \Theta_{i}} + {N_{0}I}} \right)^{- 1}\Theta_{i}^{H}H^{H}\Phi_{i}^{H}} = {{{\Theta_{i}^{H}\left( {{H^{H}H} + {N_{0}I}} \right)}^{- 1}H^{H}\Phi_{i}^{H}} = {{\Theta_{i}^{H}\left( {L^{- H}D^{- 1}L^{- 1}H^{H}} \right)}{\Phi_{i}^{H}.}}}}}} & (42)\end{matrix}$

All acronyms defined in the above description additionally hold in allclaims included herein.

While the Disclosure has been particularly shown and described withreference to specific embodiments, it should be understood by thoseskilled in the art that various changes in form and detail may be madetherein without departing from the spirit and scope of the Disclosure asdefined by the appended claims. The scope of the Disclosure is thusindicated by the appended claims and all changes which come within themeaning and range of equivalency of the claims are therefore intended tobe embraced.

In example 1, a method adapted for performing MIMO detection in a mobilecommunication device is disclosed, the method comprising:

-   performing wireless communication via a transceiver of the mobile    communication device;-   generating a demodulation reference signal based on a first    plurality of symbols of the wireless communication;-   generating a channel estimation matrix based on the demodulation    reference signal;-   inverting the channel estimation matrix to obtain a channel    pseudo-inverse matrix;-   generating a tracking reference signal based on a second plurality    of symbols of the wireless communication;-   calculating a phase shift for one or more additional symbols based    on the tracking reference signal;-   determining a corrected channel pseudo-inverse matrix for the one or    more additional symbols by adjusting the channel pseudo-inverse    matrix according to the calculated phase shift; and-   controlling the transceiver to perform data detection on one or more    orthogonal frequency division multiplexing subcarriers based on the    corrected channel pseudo-inverse matrix.

In example 2, the method of example 1 is disclosed, wherein the wirelesscommunication is received on a multiple-input and multiple-outputnetwork.

In example 3, the method of example 1 or 2 is disclosed, wherein thewireless communication is a multiple-input and multiple-output wirelesscommunication.

In example 4, the method of any one of examples 1 to 3 is disclosed,further comprising receiving the wireless communication on a pluralityof receive antennas.

In example 5, the method of any one of examples 1 to 4 is disclosed,further comprising receiving the wireless communication from a pluralityof transmission antennas.

In example 6, the method of example 4 is disclosed, wherein theplurality of receive antennas are synchronous.

In example 7, the method of example 4 is disclosed, wherein theplurality of receive antennas are asynchronous.

In example 8, the method of example 5 is disclosed, wherein theplurality of transmission antennas are synchronous.

In example 9, the method of example 5 is disclosed, wherein theplurality of transmission antennas are asynchronous.

In example 10, the method of any one of examples 4 to 9 is disclosed,wherein the plurality of transmission antennas and/or receive antennasare a plurality of Multiple Input Multiple Output (“MIMO”) transmitantennas and a plurality MIMO receive antennas.

In example 11, the method of any one of examples 1 to 10 is disclosed,further comprising transmitting the wireless communication from aplurality of asynchronous transmitters and receiving the wirelesscommunication on a plurality of synchronous receivers.

In example 12, the method of any one of examples 1 to 10 is disclosed,further comprising receiving the wireless communication from a pluralityof synchronous transmitters and receiving the wireless communication ona plurality of asynchronous receivers.

In example 13, the method of any one of examples 1 to 10 is disclosed,further comprising receiving the wireless communication from a pluralityof asynchronous transmitters and receiving the wireless communicationwith a plurality of asynchronous receivers.

In example 14, the method of any one of examples 1 to 13 is disclosed,wherein the demodulation reference signal is received on one or moreorthogonal frequency division multiplexing symbols.

In example 15, the method of example 14 is disclosed, further comprisingreceiving the demodulation reference signal on one or more orthogonalfrequency division multiplexing symbols per subcarrier per subframe.

In example 16, the method of example 14 or 15 is disclosed, furthercomprising receiving the demodulation reference signal on only oneorthogonal frequency division multiplexing symbol per subcarrier persubframe.

In example 17, the method of any one of examples 14 to 16 is disclosed,wherein the demodulation reference signal is a single, frontloadeddemodulation reference signal.

In example 18, the method of any one of examples 14 to 17 is disclosed,wherein the demodulation reference signal is received on a plurality ofsubcarriers.

In example 19, the method of any one of examples 14 to 18 is disclosed,wherein the demodulation reference signal is received on a physicaluplink control channel.

In example 20, the method of any one of examples 14 to 18 is disclosed,wherein the demodulation reference signal is received on a physicaluplink shared channel.

In example 21, the method any one of examples 1 to 20 is disclosed,wherein the wireless communication further comprises a trackingreference signal.

In example 22, the method of any one of examples 1 to 21 is disclosed,further comprising receiving the tracking reference signal on a physicaluplink control channel.

In example 23, the method of any one of examples 1 to 22 is disclosed,further comprising receiving the tracking reference signal on a physicaluplink shared channel.

In example 24, the method of any one of examples 1 to 23 is disclosed,wherein the tracking reference signal is received on each symbol of asingle subcarrier within a subframe.

In example 25, the method of any one of examples 1 to 24 is disclosed,wherein the tracking reference signal is received on fewer than eachsymbol of a single subcarrier within a subframe.

In example 26, the method of any one of examples 1 to 23 or 25 isdisclosed, wherein the tracking reference signal is received on symbolsfour through fourteen of a single subcarrier within a subframe.

In example 27, the method of any one of examples 1 to 23 or 25 isdisclosed, wherein the tracking reference signal is received on symbolsthree through thirteen of a single subcarrier within a subframe.

In example 28, the method of any one of examples 1 to 27 is disclosed,further comprising creating the channel estimation matrix from thedemodulation reference signal using a channel estimator.

In example 29, the method of any one of examples 1 to 28 is disclosed,wherein the channel estimation matrix comprises a quantity of rows, saidquantity corresponding to a quantity of receive antennas for thewireless communication.

In example 30, the method of any one of examples 1 to 29 is disclosed,wherein the channel estimation matrix comprises a quantity of columns,said quantity corresponding to a quantity of transmit antennas for thewireless communication.

In example 31, the method of any one of examples 1 to 30 is disclosed,wherein a first dimension of the channel estimate matrix corresponds toa quantity of receive antennas, and a second dimension of the channelestimate matrix corresponds to a quantity of transmit antennas.

In example 32, the method of any one of examples 1 to 31 is disclosed,wherein the wireless communication is divided into a plurality ofsubframes, and wherein the channel estimate matrix is calculated onceper subframe.

In example 33, the method of example 32 is disclosed, wherein thechannel estimate matrix is calculated in response to a receipt of thedemodulation reference signal.

In example 34, the method of any one of examples 1 to 33 is disclosed,wherein obtaining the channel pseudo-inverse matrix further comprisesisolating each of a plurality of encoded signal data symbols from thewireless communication based on the channel estimation matrix.

In example 35, the method of example 34 is disclosed, wherein isolatingeach of the plurality of encoded signal data symbols from the wirelesscommunication based on the channel estimation matrix includes generatingan equalization filter based on the channel estimation matrix andapplying the equalization filter to the wireless communication.

In example 36, the method of example 34 or 35 is disclosed, furthercomprising a shared time-frequency channel, said shared time-frequencychannel comprising a plurality of channels between a plurality oftransmit antennas and a plurality of receive antenna, and furthercomprising determining a channel estimation matrix for each of theplurality of channels, and isolating each of a plurality of encodedsignal data units from combined signal data based on the channelestimates for the plurality of channels.

In example 37, the method of any one of examples 1 to 36 is disclosed,further comprising using the created channel estimation matrix toperform a MIMO detection to estimate the symbols transmitted.

In example 38, the method of any one of example 37 is disclosed, furthercomprising performing the MIMO detection with a zero-forcing equalizeralgorithm.

In example 39, the method of example 37 is disclosed, further comprisingperforming the MIMO detection with a minimum mean square errorequalizer.

In example 40, the method of any one of examples 1 to 39 is disclosed,wherein the tracking reference signal is a Phase Noise CompensationReference Signal.

In example 41, the method of example 40 is disclosed, wherein the PhaseNoise Compensation Reference Signal is included for use in 5G.

In example 42, the method of any one of examples 1 to 41 is disclosed,wherein the phase shift results from phase noise.

In example 43, the method of any one of examples 1 to 41 is disclosed,wherein the phase shift results from Doppler effect.

In example 44, the method of any one of examples 40 to 43 is disclosed,further comprising the wireless communication being carried on awavelength with increased susceptibility to phase noise compared to aRadio Access Technology operating on a longer wavelength.

In example 45, the method of any one of examples 1 to 44 is disclosed,further comprising creating a tracking reference signal matrix.

In example 46, the method of example 45 is disclosed, further comprisingadjusting the channel pseudo-inverse matrix by calculating a Hadamardproduct of the pseudo-inverse matrix and the tracking reference signalmatrix.

In example 47, the method of example 46 is disclosed, wherein thecorrected channel pseudo-inverse matrix is a detected channel that hasbeen corrected for phase noise.

In example 48, the method of any one of examples 1 to 47 is disclosed,further comprising receiving the wireless communication on a 5G network.

In example 49, the method of any one of examples 1 to 48 is disclosed,further comprising receiving the wireless communication on one or moretransmission subframes is disclosed, wherein each of the one or moretransmission subframes is shorter than one millisecond.

In example 50, the method of any one of examples 1 to 49 is disclosed,wherein the wireless communication comprises a channel, and wherein thechannel remains acceptably stable throughout the subframe.

In example 51, the method of example 50 is disclosed, wherein thechannel stability permits calculation of fewer channel pseudo-inversematrices per subframe compared to legacy radio access technology.

In example 52, the method of any one of examples 1 to 51 is disclosed,wherein the wireless communication occurs in a downlink scenario.

In example 53, the method of any one of examples 1 to 51 is disclosed,wherein the wireless communication occurs in an uplink scenario.

In example 54, the method of any one of examples 1 to 53 is disclosed,further comprising receiving a demodulation reference signal on a firstsubcarrier during an orthogonal frequency-division multiplexing symbolperiod.

In example 55, the method of any one of examples 1 to 54 is disclosed,further comprising generating a channel detection matrix based on thedemodulation reference signal.

In example 56, the method of any one of examples 1 to 55 is disclosed,further comprising receiving the tracking reference signal on aplurality of subcarriers.

In example 57, the method of any one of examples 1 to 56 is disclosed,further comprising rotating a channel pseudo-inverse matrix according tothe phase shift to obtain a corrected channel pseudo-inverse matrix fora second symbol period.

In example 58, the method of examples 57 is disclosed, furthercomprising rotating a first corrected channel pseudo-inverse matrixaccording to the phase shift to obtain a second corrected pseudo-inversematrix for a second symbol period.

In example 59, the method of any one of examples 1 to 58 is disclosed,further comprising performing a MIMO detection on a data symbol receivedafter calculating the channel pseudo-inverse matrix, the MIMO detectionbeing performed in accordance with the channel pseudo-inverse matrix andadjusted in accordance with the phase shift.

In example 60, the method of any one of examples 1 through 59 isdisclosed, wherein the first plurality of symbols is a plurality ofdemodulated reference symbols.

In example 61, the method of any one of examples 1 through 60 isdisclosed, wherein the second plurality of symbols is a plurality oftracking reference symbols.

In example 62, the method of any one of examples 1 through 61 isdisclosed, further comprising receiving demodulation reference symbolson a plurality of subcarriers.

In example 63, the method of example 62 is disclosed, further comprisinggenerating a channel detection matrix based on the demodulationreference signal for each of the demodulation reference symbols receivedon the plurality of subcarriers.

In example 64, the method of any of examples 1-61 is disclosed, furthercomprising using a method of matrix decomposition to invert the channelestimation matrix to obtain a channel pseudo-inverse matrix.

In example 65, the method of any of example 64 is disclosed, furthercomprising the method of matrix decomposition being QR Decomposition.

In example 66, the method of example 64 is disclosed, further comprisingthe method of matrix decomposition being Lower-Upper Decomposition.

In example 67, the method of example 64 is disclosed, further comprisingthe method of matrix decomposition being a Cholesky decomposition.

In example 68, the method of example 64 is disclosed, further comprisingthe method of matrix decomposition being LDL Decompensation.

In example 69, the method of example 64 is disclosed, further comprisingthe method of matrix decomposition being Eigenvalue Decompensation.

In example 70, the method of example 64 is disclosed, further comprisingthe method of matrix decomposition being Singular Value Decompensation.

In example 71, an apparatus is disclosed, including circuitry,configured to perform the method of any one of examples 1 through 70.

In example 72, a user device is disclosed, configured to perform themethod of any one of examples 1 through 70.

In example 73, a device is disclosed, including, but not limited to, acomputer, a desktop computer, a smartphone, a wearable device, a motorvehicle, an appliance, a home management system, a positioning system, amapping system, or any other device with a wireless network connection,configured to perform the method of any one of examples 1 through 70.

In example 74, a device is disclosed configured to connect to a wirelessnetwork through 5th Generation Wireless, configured to perform themethod of any one of examples 1 through 70.

In example 75, a MIMO device is disclosed, including, but not limited toa base station, configured to perform the method of any one of examples1 through 70.

In example 76, an apparatus for wireless communication is disclosed,said apparatus comprising:

-   a transceiver, configured to perform a wireless communication    comprising a demodulation reference signal and a tracking reference    signal;-   a signal processing circuit configured to generate a channel    estimation matrix for the wireless communication; and-   a phase calculation circuit configured to determine a phase shift of    the wireless communication based on a tracking reference signal;-   wherein the signal processing circuit is further configured to    generate a channel estimation matrix based on the received    demodulation reference signal and to invert the channel estimation    matrix to obtain a channel pseudo-inverse matrix;-   wherein the phase calculation circuit is further configured to    generate a phase shift for one or more additional symbols based on    the tracking reference signal and to determine a corrected channel    pseudo-inverse matrix by adjusting the channel pseudo-inverse matrix    according to the calculated phase shift; and wherein the signal    processing circuit is further configured to perform data detection    on one or more orthogonal frequency division multiplexing    subcarriers based on the corrected channel pseudo-inverse matrix.

In example 77, a processing circuit arrangement for a wirelesscommunication is disclosed, said processing circuit arrangementcomprising an antenna, configured to receive a wireless communicationcomprising a demodulation reference signal and a tracking referencesignal;

-   a signal processing circuit configured to create a channel    estimation matrix for the wireless communication; and-   a phase calculation circuit configured to calculate a phase shift of    the wireless communication using a tracking reference signal;-   wherein the signal processing circuit creates a channel estimation    matrix based on the received demodulation reference signal and    inverts the channel estimation matrix to obtain a channel    pseudo-inverse matrix;-   wherein the phase calculation circuit calculates a phase shift for    one or more additional symbols based on the tracking reference    signal and determines a corrected channel pseudo-inverse matrix by    adjusting the channel pseudo-inverse matrix according to the    calculated phase shift; and wherein the signal processing circuit    performs data detection on one or more orthogonal frequency division    multiplexing subcarriers using the corrected channel pseudo-inverse    matrix.

In example 78, the subject matter of examples 76 or 77 is disclosed,further comprising the phase calculation circuit rotating the channelpseudo-inverse matrix based on a plurality of calculated phase shifts toobtain a plurality of corrected channel estimation matrices.

In example 79, the subject matter of any one of examples 76 to 78 isdisclosed, further comprising a plurality of multiple input multipleoutput receive antennas, which receive wireless communication from aplurality of multiple input multiple output transmit antennas.

In example 80, the apparatus of examples 76 through 79 is disclosed,configured as a user equipment.

In example 81, the apparatus of any one of examples 76 through 79 isdisclosed, configured as a user device, including, but not limited to, acomputer, a desktop computer, a smartphone, a wearable device, or anyother user device with a wireless network connection.

In example 82, the apparatus of any one of examples 76 through 79 isdisclosed, configured as a motor vehicle, an appliance, a homemanagement system, a positioning system, a mapping system, or any otherdevice with a wireless network connection.

In example 83, the apparatus of any one of examples 76 through 82 isdisclosed, configured to connect to a wireless network through 5G.

In example 84, the subject matter of any one of examples 76 through 83is disclosed, further comprising the signal processing circuit beingconfigured to process the wireless communication to obtain a firstplurality of symbols comprising the demodulation reference signal and tocalculate a channel for the wireless communication using thedemodulation reference signals.

In example 85, the subject matter of example 84 is disclosed, wherein ashared time-frequency channel is composed of a plurality of channelsbetween a plurality of transmit antennas and a plurality of receiveantennas, and wherein the signal processing circuit is configured todetermine a channel estimate for each of the plurality of channels.

In example 86, the subject matter of example 85 is disclosed, such thatsaid subject matter can optionally include wherein the plurality oftransmit antennas are a plurality of Multiple Input Multiple Outputtransmit antennas and the plurality of receive antennas are a pluralityof Multiple Input Multiple Output receive antennas.

In example 87, a means for decoding a wireless communication isdisclosed, wherein said means performs any one of method 1 through 70.

In example 88, Machine-readable storage including machine-readableinstructions is disclosed, when executed, to implement a method orrealize an apparatus as disclosed in any preceding example.

In example 89, a method of performing matrix decomposition in amultiple-input multiple-output system with tracking is disclosed, saidmethod comprising:

-   receiving a wireless communication via a receiver of a mobile    communication device; deriving a demodulation reference signal from    a first plurality of symbols of the wireless communication;-   creating a channel estimation matrix using the demodulation    reference signal; calculating a decompensation matrix of the channel    estimation matrix;-   deriving a tracking reference signal from a second plurality of    symbols of the wireless communication;-   calculating a phase shift for one or more additional symbols based    on the tracking reference signal; and-   determining a corrected decompensation matrix for the one or more    additional symbols by adjusting the decompensation matrix according    to the calculated phase shift.

In example 90, the method of example 89 is disclosed, further comprisingcalculating the decompensation matrix using QR Decomposition.

In example 91, the method of example 89 is disclosed, further comprisingcalculating the decompensation matrix using Lower-Upper Decomposition.

In example 92, the method of example 89 is disclosed, further comprisingcalculating the decompensation matrix using Cholesky decomposition.

In example 93, the method of example 89 is disclosed, further comprisingcalculating the decompensation matrix using LDL Decompensation.

In example 94, the method of example 89 is disclosed, further comprisingcalculating the decompensation matrix using Eigenvalue Decompensation.

In example 95, the method of example 89 is disclosed, further comprisingcalculating the decompensation matrix using Singular ValueDecompensation.

In example 96, the example XYZ is disclosed, the method of any one ofexamples 89 through 95 is disclosed, further comprising thedecompensation matrix being a noise whitening filter.

In example 97, the method of any one of examples 89 through 95 isdisclosed, further comprising the decompensation matrix being a maximumlikelihood detector.

In example 98, the method of any one of examples 89 through 95 isdisclosed, further comprising the decompensation matrix being a treesearch detector.

In example 99, the method of any one of examples 89 through 95 isdisclosed, further comprising the decompensation matrix being apseudo-inverse matrix.

In example 100, the method of any one of examples 89 through 95 isdisclosed, further comprising the decompensation matrix being a lineardetector.

In example 101, the method of example 89 is disclosed, furthercomprising calculating the decompensation matrix using one of QRDecomposition, Lower-Upper Decomposition, Cholesky decomposition, LDLDecompensation, Eigenvalue Decompensation, or Singular ValueDecompensation.

What is claimed is:
 1. A method adapted for performing MIMO detection ina mobile communication device, the method comprising: performingwireless communication via a transceiver of the mobile communicationdevice; generating a demodulation reference signal based on a firstplurality of symbols of the wireless communication; generating a channelestimation matrix based on the demodulation reference signal; invertingthe channel estimation matrix to obtain a channel pseudo-inverse matrix;generating a tracking reference signal based on a second plurality ofsymbols of the wireless communication; calculating a first phase shiftbased on the tracking reference signal; adjusting the channelpseudo-inverse matrix for a symbol within a subframe according to thecalculated first phase shift; and calculating a second phase shift basedon the tracking reference signal; adjusting said channel pseudo-inversematrix for a subsequent symbol within the subframe according to thecalculated second phase shift.
 2. The method of claim 1, wherein thewireless communication is received on a multiple-input andmultiple-output network.
 3. The method of claim 1, wherein a firstdimension of the channel estimate matrix corresponds to a quantity ofreceive antennas, and a second dimension of the channel estimate matrixcorresponds to a quantity of transmit antennas.
 4. The method of claim1, wherein obtaining the channel pseudo-inverse matrix further comprisesisolating each of a plurality of encoded signal data symbols from thewireless communication based on the channel estimation matrix.
 5. Themethod of claim 1, further comprising using the generated channelestimation matrix to perform a MIMO detection to estimate the symbolstransmitted.
 6. The method of claim 5, further comprising performing theMIMO detection with a zero-forcing equalizer algorithm.
 7. The method ofclaim 5, further comprising performing the MIMO detection with a minimummean square error equalizer.
 8. The method of claim 1, wherein thetracking reference signal is a Phase Noise Compensation ReferenceSignal.
 9. The method of claim 1, further comprising adjusting thechannel pseudo-inverse matrix by calculating a Hadamard product of thechannel pseudo-inverse matrix and the generated tracking referencesignal.
 10. The method of claim 1, further comprising rotating a channelpseudo-inverse matrix according to the phase shift to obtain a correctedchannel pseudo-inverse matrix for a second symbol period.
 11. The methodof any of claim 1, further comprising using a method of matrixdecomposition to invert the channel estimation matrix to obtain achannel pseudo-inverse matrix.
 12. The method of claim 11, furthercomprising the method of matrix decomposition being QR Decomposition.13. The method of claim 11, further comprising the method of matrixdecomposition being Lower-Upper Decomposition.
 14. The method of claim11, further comprising the method of matrix decomposition being aCholesky decomposition.
 15. The method of claim 11, further comprisingthe method of matrix decomposition being LDL Decompensation.
 16. Themethod of claim 11, further comprising the method of matrixdecomposition being Eigenvalue Decompensation.
 17. The method of claim11, further comprising the method of matrix decomposition being SingularValue Decompensation.
 18. A processing circuit arrangement for awireless communication, said processing circuit arrangement comprising atransceiver, configured to receive a wireless communication comprising ademodulation reference signal and a tracking reference signal; a signalprocessing circuit configured to create a channel estimation matrix forthe wireless communication; and a phase calculation circuit configuredto calculate a phase shift of the wireless communication using atracking reference signal; wherein the signal processing circuit createsa channel estimation matrix based on the demodulation reference signaland inverts the channel estimation matrix to obtain a channelpseudo-inverse matrix; wherein the phase calculation circuit calculatesa first phase shift based on the tracking reference signal and adjuststhe channel pseudo-inverse matrix for a symbol within a subframeaccording to the phase shift; and calculates a second phase shift basedon the tracking reference signal; adjusts said channel pseudo-inversematrix for a subsequent symbol without the subframe according to thecalculated second phase shift.
 19. The processing circuit arrangement ofclaim 18, further comprising the phase calculation circuit rotating thechannel pseudo-inverse matrix based on a plurality of calculated phaseshifts to obtain a plurality of corrected channel estimation matrices.20. A method of performing matrix decomposition in a multiple-inputmultiple-output system with tracking, said method comprising: receivinga wireless communication via a receiver of a mobile communicationdevice; deriving a demodulation reference signal from a first pluralityof symbols of the wireless communication; creating a channel estimationmatrix using the demodulation reference signal; calculating adecompensation matrix of the channel estimation matrix; deriving atracking reference signal from a second plurality of symbols of thewireless communication; calculating a first phase shift for one or moreadditional symbols based on the tracking reference signal; and adjustingthe decompensation matrix for a symbol within a subframe according tothe calculated first phase shift; and calculating a second phase shiftbased on the tracking reference signal; and adjusting saiddecompensation matrix for a subsequent symbol within the subframeaccording to the calculated second phase shift.
 21. The method of claim20, further comprising the decompensation matrix being a noise whiteningfilter.
 22. The method of claim 20, further comprising thedecompensation matrix being a maximum likelihood detector.
 23. Themethod claim 20, further comprising calculating the decompensationmatrix using one of QR Decomposition, Lower-Upper Decomposition,Cholesky decomposition, LDL Decompensation, Eigenvalue Decompensation,or Singular Value Decompensation.